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Q₈⋊C₈×C₁₄₉ #23749083

order	9536
nilpotency class	3
isoclinism	isoclinic class of D₈
automorphism	?
homology	Abelianization (H₁) = C₂×C₈×C₁₄₉ · Schur multiplier (H₂) = C₂

Aliases

direct product	Q₈⋊C₈×C₁₄₉
unambiguous semidirect product	Q₈⋊(C₈×C₁₄₉)

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₄₉	D₄
commutator	C₄	C₂×C₈×C₁₄₉
Frattini, cosocle	C₄²	C₂²×C₁₄₉
socle, prime radical	C₂²×C₁₄₉	C₂²⋊C₄
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₄₉ ◁ C₄²×C₁₄₉ ◁ G

70 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

4172 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	Q₈⋊C₈×D₁₄₉, #34043072, #34043077, …
maximal subgroup of	C₂×Q₈⋊C₈×C₁₄₉, #1476×C₁₄₉, #1477×C₁₄₉, …
maximal normal subgroup of	C₂×Q₈⋊C₈×C₁₄₉, #1476×C₁₄₉, #1477×C₁₄₉, …
maximal quotient of	#1271×C₁₄₉, #1272×C₁₄₉, #1279×C₁₄₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9536, 7);